Edge Detection - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 177

To obtain an optimum value of λ, the intuitionistic fuzzy entropy ( IFE ) is
used.
After the introduction of the non-probabilistic entropy and fuzzy entropy,
different types of entropies are given by many authors using intuitionistic
fuzzy set theory. In this method, the IFE as given by Vlachos and Sergiadis
[20] is used and is written as

1 1

−
∑ 1

N M −

2

1 2 μν ()() ()

() ()

g g + π g

Aij Aij Aij

IFEA (;) λ = (8.5)

2 2 2 (()

NM × π g + μ g + ν g ij

Aij A ij A

i = 1 j =

IFE is calculated for all the λ values. The optimum value of λ that corre-
sponds to the maximum value of entropy is computed as

λ

opt = max( (;))

IFEA λ

With the λ value known, the intuitionistic fuzzy membership degrees of the
pixels are computed and an intuitionistic fuzzy image is formed.
Then the median filter of size 3 × 3 is applied over the intuitionistic fuzzy
image. The corresponding area of the image covered by the median filter is
the image window. The median value, surrounding the current pixel A ( m , n )
of the image window, is computed as

Zmn (,) = median { A minj ij mn ( − , − )}, (, ) ∈ φ ( ,)

where
ϕ( m , n ) is the window
m = 1, 2, …, M ;

n = 1, 2, …, N

Total variation in the 3 × 3 image window with respect to the median of the
window is computed as

∑

(8.6)

Imn (,) = abs Ai j Zmn ( (, ) − ( , )

ijW , ∈

where
i and j are the pixels in the 3 × 3 window
W is the window